Visiting goalkeeper Sergio Herrera turned in a stunning display that threatened to make it a fourth straight top-flight game without taking three points for Diego Simeone's men.
"It's our last game of the year here. It was important to win it," Morata said on the Wanda Metropolitano pitch afterwards, before talking up Atleti's recent performance.
"We had a lot of chances - not just me, the whole team. I think we're growing as a team.
"Every team needs to win. We're in a good dynamic, we’ve got a lot of desire and, as I say, we're growing as a team. The results will come."
As Diego Costa remains on the sidelines with a neck injury, Atletico have been linked to a host of strikers ahead of the January transfer window.
Even if the likes of Edinson Cavani, Timo Werner and Olivier Giroud are under consideration, Morata insists that is none of his concern.
"No, I don't care," he replied. "We're a great team and great dressing room and that's the important thing."